2y(y-1)=7y-7

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Solution for 2y(y-1)=7y-7 equation: 


Simplifying
2y(y + -1) = 7y + -7

Reorder the terms:
2y(-1 + y) = 7y + -7
(-1 * 2y + y * 2y) = 7y + -7
(-2y + 2y2) = 7y + -7

Reorder the terms:
-2y + 2y2 = -7 + 7y

Solving
-2y + 2y2 = -7 + 7y

Solving for variable 'y'.

Reorder the terms:
7 + -2y + -7y + 2y2 = -7 + 7y + 7 + -7y

Combine like terms: -2y + -7y = -9y
7 + -9y + 2y2 = -7 + 7y + 7 + -7y

Reorder the terms:
7 + -9y + 2y2 = -7 + 7 + 7y + -7y

Combine like terms: -7 + 7 = 0
7 + -9y + 2y2 = 0 + 7y + -7y
7 + -9y + 2y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
7 + -9y + 2y2 = 0

Factor a trinomial.
(1 + -1y)(7 + -2y) = 0


Subproblem 1
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1y = 0 + -1
-1y = 0 + -1

Combine like terms: 0 + -1 = -1
-1y = -1

Divide each side by '-1'.
y = 1

Simplifying
y = 1

Subproblem 2
Set the factor '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {1, 3.5}

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